We propose a flexible design for the identification of optimal dose combinations in dual-agent dose-finding clinical trials. The design is called AAA, standing for three adaptations: adaptive model selection, adaptive dose insertion, and adaptive cohort division. The adaptations highlight the need and opportunity for innovation for dual-agent dose finding and are supported by the numerical results presented in the proposed simulation studies. To our knowledge, this is the first design that allows for all three adaptations at the same time. We find that AAA enhances the chance of finding the optimal dose combinations and shortens the trial duration. A clinical trial is being planned to apply the AAA design and a web tool is being developed for both statisticians and non-statisticians.